IOMAC'13iomac.eu/iomac/2013/IOMAC_Guimaraes/files/papers...1.1.2. Wind Turbine The bucket foundation is placed below a fully operational Vestas V90-3.0 MW offshore wind turbine with

IOMAC'13

5th International Operational Modal Analysis Conference

2013 May 13-15 Guimarães - Portugal

DAMPING ESTIMATION OF A PROTOTYPE

BUCKET FOUNDATION FOR OFFSHORE WIND

TURBINES IDENTIFIED BY FULL SCALE TESTING

Mads Damgaard1, Lars Bo Ibsen

2, Lars V. Andersen

3, Palle Andersen

4, Jacob K. F. Andersen

5

ABSTRACT

Wave loading misaligned with wind turbulence often introduces large fatigue loads on offshore wind

turbine structures. In this particular case, the structure is sensitive to resonant excitation acting out of

the wind direction due to a small aerodynamic damping contribution in the cross-wind direction.

Therefore, in order to assess the fatigue damage accumulation during the lifetime of the offshore wind

turbine structure, a correct estimation of the cross-wind modal damping is necessary. This paper

describes the cross-wind modal damping of the lowest eigenmode of a fully operational Vestas V90-

3.0 MW offshore wind turbine installed on a prototype bucket foundation. The foundation and the

turbine tower are equipped with a monitoring system with 15 Kinemetrics force balance

accelerometers and a Digitexx acquisition system. Using free vibration decays from “rotor-stop” tests

and operational modal techniques, the cross-wind modal damping is estimated on a regular basis.

Analyses show maximum cross-wind damping at rated wind speed. For higher wind speeds decreasing

damping is observed, mainly due to blade pitch activation. In addition, a high structural acceleration

level is needed to activate the soil damping.

Keywords: Free vibration decay, Frequency Domain Decomposition, offshore wind turbines,

Operational Modal Analysis, Stochastic Subspace Identification, system identification.

1. INTRODUCTION

Wind energy is expected to be a dominating energy source in the coming years. The increased size of

the offshore wind turbines and the demand for cost-effective turbines mean that the turbine system has

become more flexible and thus more dynamically active – even at low frequencies. Therefore, the

excitation frequencies related to waves and turbine blades passing the tower are close to the structural

resonance frequency. In order to obtain a reliable estimate of the fatigue life of the wind turbine

structure, the structural dynamic properties must be analysed. Contrary to civil engineering structures

1 Industrial PhD Fellow, Vestas Turbines R&D, [email protected]

2 Professor, Department of Civil Engineering, Aalborg University, [email protected]

3 Associate Professor, Department of Civil Engineering, Aalborg University, [email protected]

4 Managing Director, Structural Vibration Solutions, [email protected]

5 Manager, Vestas Turbines R&D, [email protected]

M. Damgaard, L. Bo Ibsen, L. V. Andersen, P. Andersen, Jacob K. F. Andersen

2

like high-rise buildings, dams and cable-stayed or suspension bridges, wind turbine structures are

exposed to periodic loading from the rotor blades, and in the presence of emergency stop or too high

wind velocity the rotor blades pitch out of the wind. The blades thus have to be able to turn around

their longitudinal axis. The variable and cyclic loads on the rotor, the tower and the foundation call for

a full appreciation of the dynamic behaviour of the wind turbine structure during its service life, i.e. an

accurate numerical model that identifies the dynamic properties of the wind turbine structure is

favourable. However, limited physical knowledge about the dynamic wind turbine system makes it

difficult to establish a mathematical model based on pure physics and fundamental laws. This in turn

justifies experimental modal analysis capable of validating and improving the numerical model [1].

An operational wind turbine is subjected to harmonic excitation from the rotor. The first excitation

frequency to consider is the rotor rotational frequency 1P. The second excitation frequency is the blade

passing frequency. For a three-bladed wind turbine, this frequency is three times the 1P frequency and

is denoted the 3P frequency. Without sufficient system damping, the resonant behaviour of the turbine

can cause severe loads inducing fatigue damage. Large fatigue loads are often observed at wind parks

characterised by a large degree of wind-wave misalignment due to a small amount of aerodynamic

damping in the cross-wind direction. However, contradictory estimates of the damping are obtained by

different authors [2], which illustrates the importance of this paper.

This chapter outlines the motivation for investigating the dynamic properties of offshore wind

turbines. Turbine characterisation and site conditions for the considered wind turbine structure are

included in the chapter. A brief introduction to different damping techniques is given in Chapter 2

with focus on the theoretical background and the practical aspects in the literature. Chapter 3 deals

with the monitoring system followed by documentation of results in Chapter 4. Finally, in Chapter 5 a

brief summary of the main findings of the present work is given with a description of what the

findings can be used for in further applications.

1.1. Wind Turbine Structure and Site Conditions

The aim of this paper is to determine the cross-wind modal damping δ1 of the lowest eigenmode

of an offshore wind turbine installed on a prototype bucket foundation in Frederikshavn, Denmark.

The wind turbine structure is a part of an offshore research test field with a total of four wind turbine

structures and has been created as a joint research and development program between the Department

of Civil Engineering at Aalborg University and Universal Foundation A/S. The following subsections

are based on [3].

1.1.1. Foundation

The bucket foundation is a welded steel structure consisting of a tubular centre column connected to a

steel bucket through flange-reinforced stiffeners. A vertical steel skirt extending down from a

horizontal base resting on the soil surface ensures the overall stabilisation by a combination of earth

pressures at the skirt and the vertical bearing capacity of the bucket. The prototype bucket foundation

is designed with a diameter of 12 m and a skirt length of 6 m. Figure 1a shows the geometry of the

bucket foundation. During the installation process, the bucket foundation penetrates the seabed due to

a combination of self-weight and applied suction. Lowering the pressure in the cavity between the

bucket and the soil surface generates a water flow, which causes the effective stresses to be reduced

around the tip of the skirt. Hence, the penetration resistance is reduced. Figure 1b shows the bucket

foundation in Frederikshavn after installation in late 2002.

1.1.2. Wind Turbine

The bucket foundation is placed below a fully operational Vestas V90-3.0 MW offshore wind turbine

with a fixed gear ratio. The turbine has a cut-in wind speed of 3.5 m/s, a rated wind speed of 15 m/s

and a cut-out wind speed of 25 m/s. The hub height is approximately 80 m, and the diameter at the

tower bottom is 4.2 m. Figure 2a and Figure 2b show the wind turbine.

5th International Operational Modal Analysis Conference, Guimarães 13-15 May 2013

3

1.1.3. Test Field

The offshore research field in Frederikshavn consists of four 2.0-3.0 MW wind turbines located next

to the harbour. Three of the turbines are located in the sea, while the investigated offshore wind

turbine structure in this paper is located in a basin with a water depth of 4 m. Geotechnical

investigations in the basin show that the soil profile primarily consists of cohesionless soils. From

seabed at level -4.1 m to -11.4 m, well graded to graded fine sand is found based on the classification

method proposed by [4]. Below this, ungraded deposit of sand and silt with varying small organic

content is identified, and below level -15 m, sand without organic content is found. The sand layer has

a unit weight γm of 19.5 kN/m3

and a relative density ID of 90%. The permeability of the sand is so

large that no pore pressure build-up appears during cyclic loading.

Figure 2 The Vestas V90-3.0 MW offshore turbine in Frederikshavn: (a) Geometry of the turbine, (b) Normal

production state. All dimensions are in millimetres.

2. EXPERIMENTAL DAMPING TECHNIQUES

In the traditional experimental modal technology, a set of frequency response functions at several

points along the structure are estimated from the measured response and excitation [5], [6]. These

functions contain all the information to determine the resonance frequencies fk, damping ratios ζk and

Figure 1 The prototype bucket foundation in Frederikshavn: (a) Geometry of the foundation concept, (b) After

installation in late 2002. All dimensions are in millimetres.


4

mode shapes of the structure. A few attempts to excite parked onshore wind turbines by

measurable excitation have been done, see [7], [8], [9]. However, for offshore wind turbines the input

excitation is difficult to measure, and the modal properties are almost impossible to estimate. In

addition, accurate modal identi-fication under actual operating conditions is difficult to extract by

traditional experimental technologies. In the following two major procedures of estimating cross-wind

modal properties of offshore wind turbines are introduced.

2.1. Free Vibration Tests

In general, the inherent modal damping in a freely vibrating system can be estimated in two ways;

either by measuring the free structural response after application of a sinusoidal load with a frequency

equal to the eigenfrequency of the structure [10] or by measuring the free structural response after the

application of an impulse. The application of an impulsive load has been reported in [2], [11], [12],

[13]. In these publications, the modal damping of offshore wind turbines has been determined by

“rotor-stop” tests. The wind turbine is effectively left to freely vibrate after the generator shuts down

and the blades pitch out of the wind. As an example, Figure 3a shows the raw output acceleration

signal for a “rotor-stop” test. As indicated in Figure 3a, the wind turbine structure behaves almost as a

single-degree-of-freedom (SDOF) system with linear viscous damping, and the corresponding

damping coefficient cv is so low that the system is undercritically damped. Wind turbine structures are

characterised by closely spaced modes occurring at nearly identical frequencies. Therefore, it is

important that the measured free decay only contains modal vibrations from one single mode as shown

in Figure 3b. The modal damping δ1 is found by least-squares fitting of a linear function to the natural

logarithm of the rate of decay of the transient response. However, modal damping estimation from free

vibration tests of wind turbines is only related to the structure. The aerodynamic effects that influence

the mode shapes are simply ignored. Therefore, a much more efficient and economical method of

estimating modal parameters of wind turbine structures is by ambient vibration tests, where the

stochastic wind excitation is used as the excitation source.

Figure 3 Raw output signal during a “rotor-stop” (a) Fore-aft tower acceleration ay as a function of time t, (b)

Fore-aft tower acceleration ay as a function of side-side acceleration ax.

2.2. Ambient Vibration Tests

Ambient modal analysis, also denoted operational modal identification, allows determination of the

inherent dynamic properties and aerodynamic effects of a structure by measuring only the structural

response and using the ambient or natural operating forces as unmeasured input. Originally,

operational modal analysis was developed for modal estimation of civil engineering structures like

buildings and bridges, where the application of the theory has been written in many excellent papers.


5

However, application of operational modal identification to operational wind turbines is not a

straightforward task. The method relies on the assumption that the system is time invariant, which is

violated for a wind turbine. The nacelle rotates about the tower, the rotor rotates around its axis and

the pitch of the blades may change. A way to handle this problem is to find a suitable period, where

blade pitch angle θb, wind speed vwind and rotor speed vrotor remain unchanged. Moreover, steady state

broadband random excitation is assumed in operational modal identification. Wind excitation fulfils

this requirement, but deterministic signals introduced by the harmonic frequencies 1P and 3P will take

place. For non-parametric methods in the frequency domain, these harmonics must be identified and

separated from the structural modes. For time-domain methods, where the modal parameters are

extracted directly by fitting parameters to the raw time histories, the harmonics are just estimated as

very highly damped modes and do not need to be filtered out. Several robust operational modal

identification methods have been developed in the past, see [14], [15] for a detailed literature review.

In this paper, two techniques are considered in order to evaluate the cross-wind modal damping δ1 of

the wind turbine in Frederikshavn; the Enhanced Frequency Domain Decomposition technique and the

Stochastic Subspace Identification technique. A short introduction to the two techniques is given

below.

2.2.1. Enhanced Frequency Domain Decomposition

The Enhanced Frequency Domain Decomposition (EFDD) technique is a non-parametric frequency

domain method and is an extension of the Basic Frequency Domain (BFD) technique [16]. As the

input excitation is assumed stationary, zero mean Gaussian white noise, the response is also Gaussian

distributed. Hence, the system response is completely described by its covariance function or auto and

cross spectra. From the linear dynamic theory [17], the system response is a linear combination of the

mode shape multiplied by the modal coordinate

(1)

Inserting Eq. (1) into the expression of the covariance function provides

(2)

where the superscript H denotes the complex conjugate transpose and the superscript T is the non-

conjugated transpose. The spectral density function for each known discrete circular frequency can

be obtained by Fast Fourier Transformation (FFT) of Eq. (2):

(3)

The spectral density function is often estimated using the Welch method [18], where the

time records are divided into nd contiguous data segments. It is beneficial to use a window function to

reduce the leakage introduced by the FFT with an overlap between segments to compensate for the

loss of information due to tapering of the data segments when the segments are multiplied by the

window function. The objective is now to decouple the Hermitian spectral density function

and describe it by superposition of single-degree-of-freedom (SDOF) systems, each corresponding to

an individual mode. The decomposition is done by taking the Singular Value Decomposition (SVD) of

each output spectral density matrix ,

(4)

where is the singular value diagonal matrix of the scalar singular values , and

is a unitary matrix of the singular vectors . It should be noticed that Eq. (4)

has the same form as Eq. (3). Assuming a white noise excitation, i.e. a diagonal spectral input matrix,

a lightly damped structure and geometrically orthogonal mode shapes for closely spaced modes, it is

shown in [16] that, near a peak in the frequency spectrum, the first singular vector is an estimate of

the mode shape , and the corresponding singular value is the auto power spectral density function

of the corresponding SDOF system. The SDOF auto power spectral density function around the peak


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is identified by comparing the estimated mode shape with the singular vectors for the

frequencies around the mode. Using a MAC criterion [19], an auto spectral bell function can be found.

The modal damping δk is then easily obtained by transforming the auto spectral bell function to time

domain by inverse FFT. Finally, to improve the estimated mode shape , the singular vectors that

correspond to the singular values in the SDOF spectral bell function are averaged jointly. The average

is weighted by multiplying the singular vectors with their corresponding singular value, i.e. singular

vectors close to the peak of the SDOF spectral bell have a large influence on the mode shape estimate.

2.2.2. Stochastic Subspace Identification

The Stochastic Subspace Identification (SSI) techniques are all formulated and solved using linear

state space formulations [20] given by

(5)

(6)

where Eq. (5) is called the state equation that models the dynamic behaviour (position and velocity) of

the physical system, and Eq. (6) is denoted as the observation equation. The physical system is

modelled by an n×n state matrix , where n is the model order, i.e. the number of considered

eigenvalues μ that completely characterise . By introducing a stochastic Gaussian white noise

process of dimension n×1 that represents the input driving the system dynamics, the state matrix

transforms the state of the system to a new state . The system output that can be observed is

defined by and is determined from the summation of a stochastic Gaussian white noise process

related to the measurement noise and the product of the state vector and the s×n observation matrix

. s is the number of sensor positions. The overall aim is now to determine an estimate of the system

matrix and the observation matrix for different model orders n. Based on traditional eigenvalue

analysis of linear dynamic systems [17], the modal damping δk is found from the pole λk of , and the

observable eigenvector is found from the product of the observation matrix and the eigenvector

. The estimation of and can either be performed from the measured time signals (data-driven

stochastic subspace identification) or from the correlations of the time signals (covariance-driven

subspace identification). The last-mentioned is due to the fact that it is required that the system

response is a realisation of a Gaussian distributed process with zero mean. Thus, a state space model

having the correct covariance function will be able to completely describe the statistical properties of

the system response.

In order to predict the state vector and system response in Eq. (5) and Eq. (6) optimally, an

innovation form of a Kalman Filter is used [20]

(7)

(8)

where is the Kalman gain and the vectors are called innovations. Assuming that measurements

are given for some initial time to and collected in a matrix

, the optimal predictors and are chosen defined as the mean value

of the state vector and the system response for all the measurements , respectively. This is

given by the conditional means

, (9)

(10)

where it is assumed that and are uncorrelated. The conditional mean on both sides of Eq. (5) and

Eq. (6) then reads

(11)

(12)


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By inserting Eq. (9) recursively into itself i times for each time step q and using this result in Eq. (10),

the estimated states for several values q can be written as [21]

(13)

where is denoted the extended observability matrix. This matrix can be determined by a Singular

Value Decomposition of the matrix that only includes the information of

the system response from the measurements. However, before using the SVD, is pre and

postmultiplied with weight matrices and ,

(14)

The values of and depend on the stochastic subspace identification algorithm. Both the

Unweighted Principal and Weighted Principal algorithms [20] are used in this paper. As indicated in

Eq. (14), the number of block rows in determines the size of the extended observability matrix

and thereby the maximum state space dimension as the product of block rows and the dimension of the

measured system response vector . In conclusion, the procedure of the Stochastic Subspace

Identification is as follows; firstly, establish the matrices and for a given number of block

rows based on the measurements, secondly, determine the extended observability matrices and

from Eq. (14) and finally, determine the states and using the same procedure as used for

establishing Eq. (13). Thus, assuming that it has been possible to estimate the states for n instance in

time, the dynamic system matrix and observation matrix can be found from a least regression

problem by minimising the residual .

Figure 4 Kinemetrics force balance accelero-meters: (a) Sensor positions in tower and foundation, (b) Sensor

mounting by use of magnets

3. MONITORING SYSTEM

In order to measure the modal space of the wind turbine in Frederikshavn, the tower and foundation

are equipped with a monitoring system consisting of 15 Kinemetrics force balance accelerometers,

model FBA-ES-U. A portable data acquisition system PDAQ-8 from DigiTexx Data Systems Inc. is

placed inside the turbine, and based on the Data Streamer Remote Monitoring and Acquisition

Software from Digitexx Systems Inc., real time data is collected and processed. The accelerometers

are mounted on consoles attached to the structure by magnets at four different levels. Figure 4a and

Figure 4b show the sensor position and the sensor mounting, respectively. It should be noticed that

generator speed vgen, blade pitch angle θb and wind speed vwind are gathered during the acceleration

measurements.


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4. INTERPRETATION OF MEASURED TIME SIGNALS

Results from the ambient and free vibrations tests on the wind turbine structure in Frederikshavn are

presented in the following.

Figure 5 Data presentation of test number 7: (a) Singular values for each channel as a function of the frequency,

(b) Spectogram of a channel placed in the top of the tower. The rotational rotor frequency 1P, the lowest

eigenmode and the blade passing frequencies 3P and 6P are clearly represented in the plots.

4.1. Ambient Vibration Tests

In the period primo October 2012 - ultimo November 2012, a total of 100 ambient vibration tests were

investigated for the Vestas V90-3.0 MW wind turbine. A sampling frequency of 200 Hz has been

used. However, since only the properties for the lowest eigenmode are of interest, the signals are

low–pass filtered followed by a decimation of order 160. Figure 5a and Figure 5b show the singular

values and the short-time Fourier transformation of test number 7, respectively. As indicated the

energy related to the rotational rotor frequency 1P, the lowest eigenmode and the blade passing

frequency 3P are almost independent of time during the test. As a starting point for modal parameter

estimation, the EFDD technique has been applied. As earlier mentioned, the method operates in the

frequency domain, which means that leakage will always be introduced when applying the Fourier

transformation and assuming periodicity. To reduce the leakage, long recording times of 2 hours have

been used [22], [23]. Contrary to the SSI technique, the harmonic component from the rotational rotor

frequency 1P must be separated from the structural mode in the EFFD technique. Therefore, it has

been utilised that a random response is approximately Gaussian distributed in case of multiple random

inputs, whereas a harmonic response follows a sinusoidal probability density function [18].


9

Hence, at each frequency the measurements are bandpass filtered, and a statistical test derived from a

Kurtosis calculation [24] is performed to identify the harmonic components.

In order to substantiate the cross-wind modal damping δ1 of the lowest eigenmode , the SSI

technique has been applied. Figure 6 shows the cross-wind modal damping δ1 using the EFDD

technique and SSI technique with Unweighted Principal Component (UPC) and Weighted Principal

Component (PC). As indicated, the three methods agree very well. This is supported by the MAC

values that indicate excellent agreement between the eigenmodes from the EFFD technique and the

SSI techniques with values higher than 0.95 for the main part of the measurements. As an example, the

eigenmode for test number 41 is shown in Figure 7a, which follows an elliptical trace. To verify

how well the modelled system from the SSI technique approximates the measured system, Figure 7b

shows the modelled and measured auto-spectra for test number 41. According to Figure 6, the

estimated cross-wind damping δ1 seems to reach an extreme value of approximately 0.05 at rated wind

speed. Afterwards the damping slightly decreases for higher wind speeds. By investigating the blade

pitch angle θb as function of mean wind speed vwind for each measurement, cf. Figure 8, it is clearly

observed that after rated wind speed the blade pitch angle θb increases drastically. This may in turn

reduce the fore-aft modal damping and thereby also the side-side damping due to coupling effects

Figure 6 Cross-wind modal damping δ1 of the lowest eigenmode for ambient vibration tests by use of the

Enhanced Frequency Domain Decomposition technique and the Stochastic Subspace Identification technique

with Unweighted Principal Component (UPC) and Weighted Principal Component (PC) algorithms.

Figure 7 Model outputs from the SSI-UPC technique for test number 41: (a) Side-side eigenmode , (b)

Measured and modelled auto-spectra.


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between the two closely spaced mode shapes that occur at nearly identical frequencies.

Figure 8 Blade pitch angle θb as a function of mean

wind speed vwind.

4.2. Free Vibration Tests

A total of 67 “rotor-stop” tests from the years 2004-2008 have been analysed. In general, during a

“rotor-stop”, the oscillatory deformation of the wind turbine structure is attenuated. This may be due

to a combination of geometrical damping, i.e. radiation of energy into the subsoil, sea, air and material

damping due to conversion of mechanical energy into heat. Since the water depth is approximately 4

m at the test site in Frederikshavn, the hydrodynamic damping δwater has negligible impact on the

measured system damping δ1 [2]. In addition, the aerodynamic damping δaero on the tower is

insignificant and hence, the measured system damping δ1 from the “rotor-stop” tests is mainly driven

by steel hysteretic damping δsteel and soil damping δsoil. The last-mentioned is a combination of

geometric damping and material damping due to slippage of grains with respect to each other. The

system damping δ1 as a function of the acceleration level ay during the “rotor-stop” test are shown in

Figure 9 with an R-square value of 0.95, meaning that the fit of the amplitude peaks explains 95% of

the total variation in the data about the average. With a steel hysteretic damping δsteel value of 0.01 in

terms of the logarithmic decrement [2], it can be stated that the soil damping δsoil is in the range of

0.004-0.04 logarithmic decrement for an acceleration level between 0.8 m/s2

and 2.1 m/s2. Assuming

normal distributed accelerations in the cross-wind direction during power production, the ambient

vibration tests show that the 95% quantile of the acceleration level for a mean wind speed vwind

between 5 m/s and 20 m/s is in the range of 0.02 m/s2-0.6 m/s

2. This may in turn indicate a maximum

soil damping δsoil of approximately 0.01 logarithmic decrement during power production as indicated

in Figure 9.


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Figure 9 System damping δ1 as a function of

acceleration level for the lowest bending mode

based on “rotor-stop” tests. The accelerometer placed

in the top of the turbine is used.

5. CONCLUSIONS

Experimental analysis of the cross-wind modal damping δ1 of the lowest eigenmode of an

offshore wind turbine installed on a bucket foundation has been presented. Inherent dynamic

properties and aerodynamic effects are evaluated with free and ambient vibration tests, where

frequency domain and time domain modal identification algorithms are utilized. Several interesting

conclusions can be drawn:

■ Non-parametric and parametric operational modal techniques show good agreement for the cross-

wind modal damping δ1 of an offshore wind turbine.

■ The cross-wind modal damping δ1 tends to de-crease for wind speeds vwind higher than rated wind

speed. Blade pitch regulation and the presence of coupled eigenmodes are believed to explain the

observation.

■ “Rotor-stop” tests indicate that notable soil damping δsoil in the cross-wind direction is introduced

for a significantly higher acceleration level than observed during power production.

Future work will concern comparison of the experimental modal findings with an aerodynamic model

of the turbine coupled with a lumped-parameter model of the soil and bucket foundation.

ACKNOWLEDGEMENTS

The authors are grateful for the financial support from the research project Cost Effective Monopile

Design funded by the Danish Energy-technological Development and Demonstration Program.

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Documents

IOMAC'13iomac.eu/iomac/2013/IOMAC_Guimaraes/files/papers...1.1.2. Wind Turbine The bucket foundation is placed below a fully operational Vestas V90-3.0 MW offshore wind turbine with